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Quantum machine learning (QML) is a fascinating new technology that combines classical machine learning and quantum computers in a way that it eventually accelerates the computing process in machine learning (Some, 2020). Basically machine learning is all about how classical computers learn patterns in data. But given the fact that classical computers have hit their own computational limits, at times it is out of their reach to run many machine learning algorithms faster (Louriz, 2019). On the other hand, quantum computers that are packed with incredible computational power and speed, can accelerate a number of machine learning algorithms, make data pattern learning process faster, and even compute and run many a complex machine learning operations that were otherwise out of the reach of classical computers (TensorFlow, 2020). Quantum computing relies on quantum mechanics phenomena of superposition and entanglement to do things faster, more efficiently. It is now possible to do many such things that we couldn’t have even dreamed of without quantum computers. Having recognized that the increased computational power, increased data availability, and algorithmic advances have all influenced QML techniques to provide good results in deep learning, optimization, kernel evaluation, cryptography, and quantum simulation tasks (Ciliberto et al., 2018). Currently, IBM, Google, NASA, and Microsoft are some of the global enterprises that are spearheading their R&D efforts and making significant advances in QML research.

There is only a single study by (Pande & Mulay, 2020) in the body of bibliometric literature that deals per se on the topic of quantitative assessment of QML research. In addition, there are quite a few other studies related to broader topics such as ‘quantum technologies’ (quantum computing) research and ‘machine learning’ research. Pande & Mulay in their study examined QML research and identified the trends in research during 2014-19, focusing mainly on growth parameters, identification of major countries, organizations, authors and journals involved in QML research.

In the area of quantum technologies, (Dhawan, Gupta, & Bhusan, 2018) examined 4703 global publications on quantum computing during 2007-16, with focus on identification of the top 10 countries, top 30 most productive organizations and authors, top 20 journals and 124 highly cited papers. (Tolcheev, 2018) highlighted the bibliometric characteristics of the quantum technologies literature during 2000-16 and identified and evaluated the key areas of research and the publication activities of different countries. (Gupta & Dhawan, 2020) examined global research (546 publications) in the domain of "Quantum Neural Networks" (QNN) on metrics such as publication output, document type, country, collaboration patterns, institutional and author affiliation, subjects, journal name, and citation patterns during 1990-2019, using Scopus database.

In the area of machine learning, (Dhawan, Gupta, & Singh, 2020) examined 48,455 global publications on machine learning during 2009-18, by focusing on growth rate, citations per paper, international collaborative papers, relative citation index, activity index, top productive countries, organizations, authors, journals, and highly-cited papers. (Rincon-Patino et al., 2018) studied machine learning research output during 2007-17 and identified the most notable authors, institutions, keywords, countrie s, categories, and journals. (Gupta & Dhawan, 2019b) examined 3960 Indian machine learning publications during 2006-17 using bibliometric techniques. It studies aspects such growth rate, global publications share, share of international collaborative papers, analyses of top 10 countries, top 20 organizations and authors, core source journals and subject areas. (Gupta & Dhawan, 2019a) examined global deep learning research using bibliometric indicators during 2004-17. (Cova & Pais, 2019) examined 5,279 publications (receiving 81,248 citations) on machine learning (ML) applications in different sub-fields of chemistry during 2008 - 2019.

The topics such as machine learning, quantum technologies and now quantum machine learning, of late, have been receiving national attention by various countries (including India) in terms of R&D investments and dedicated budgets. It is observed that QML as a subfield has been growing in terms of its applications especially in the last few years. It was, therefore, felt that there is a need to undertake a bibliometric study of the literature in the field, covering publications data since its beginning (1999) till date. Even as Pandey & Mulay have published recently in 2020 a study on this topic, but the fact is that their study is based on a limited publications dataset (276 and 154 publications from two separate databases), on a limited publication period span, covering just 6-year period 2014-19, and analyzed on a set of limited parameters. Given this rationale, the authors thought it prudent to carry out a comprehensive study in QML research that is based on a larger dataset, on a larger set of metrics, with the aim to describe the contemporary status of QML research at global, national, institutional, and individual author level. In addition to providing a window to key productive countries, key research organizations, key contributing authors and journals, such a study is also going to carry out a bibliometric mapping of QML literature to visually represent network relations between key authors, institutions, and countries involved in QML research.

The present study seeks to examine global publications output in the domain of quantum machine learning (QML) research with the purpose to understand the status of QML research at global, national, institutional, and individual author level, using quantitative and qualitative metrics. The data for the study has been sourced from the Scopus database covering the period 1999-2020. The study seek to evaluate the publications data in terms of (i) distribution of publications by type and source, (ii) annual and cumulative publications growth, (iii) the citation impact registered by the publications (iv) the publication profile of the top 10 most productive countries, (v) the distribution of publications by broad subjects and significant keywords, (vi) the publications profile of top 25 organizations and authors of publications, (vii) the top communications channels in the research, and (viii) the bibliographic characteristics of highly-cited papers in the subject.

The study sourced data on the topic of quantum machine learning from the Scopus database (http://www.scopus.com). The search strategy that this study used in order to identify, retrieve, and download publications metadata included using search keywords “quantum machine learning” tagged to field tags “Keyword” and “Title” (Article Title), and subsequently confined the global search output to the period ‘1999-2020’. In the subsequent rounds of data search, the global output was refined by the country name, one by one, to identify and generate a list of top 15 most productive countries in the subject. The study noted that the global output in the field of quantum machine learning for the period 1999-2020 was 1374 publications. The data was downloaded in csv file format, which was subsequently analyzed using statistical methods. In addition, the authors used analytical provisions of the Scopus database as a means to distribute the publications output by broad subject areas, collaborating countries, contributing authors, affiliating organizations, and source journals, etc. The citations to publications were counted from date of their publication till 9.2.2021. The study used bibliometric techniques and indicators as a method to quantify and evaluate the performance of the most productive countries, organizations, authors and journals. The VOSviewer and biblioshiny app for bibliometrix were used to evaluate and visualize the interaction among most productive countries/territories, organizations, authors and keywords.

(KEY (quantum machine learning) or TITLE (quantum machine learning)) and PUBYEAR > 1998 AND PUBYEAR < 2021

This study used bibliometric methods to analyze the global research in the domain of QML (1374 publications) published during 1999-2020. The study provides an overview of the status of research in quantum machine learning on a series of quantitative and qualitative metrics, and presents a visual view of network relationship between leading authors, research institutions, and collaborative countries. In addition, the study identifies the global players in QML research including as key countries, key institutions, key authors, and key subject areas of research.

The study concludes that the QML research is gradually emerging as an interdisciplinary area of research in the field of computer science. But, despite its growing importance in the academia and industry, the body of the global literature in the subject is still very small, limited to just 1374 publications which appeared in a long period 22 years during 1999-2020, with an average output of 62 publications per year. The study finds that QML as a research field is still at a nascent stage of its development. Even as participation in QML research is global, but only a select few countries dominate in global productivity in the field. For instance, the USA, China, the UK, and Germany accounted for a significantly high 75.90% share of the global output, In contrast, global share of 11 of 15 most productive countries is in single digits, it is just small and insignificant. Besides, most of top 25 centres of excellence in QML research come from such leading countries as the USA, China, UK, and Germany that dominate global productivity in the subject. The study observes that most countries in the top 15 list -- including India, Italy, Japan, Australia, South Korea, Russia Fed., France, Spain, and Austria will -- are peripheral players in global QML research. The policy makers and other stakeholders in such countries need to initiate national programmes and make fresh R&D investments aimed at strengthening research infrastructure, international collaboration, capacity building and manpower development in the domain of quantum machine learning research and thereby lead their country to come to the top the global research in the subject.

We used Scopus database for sourcing publications data for our bibliometric study. Whereas Scopus is a universally recognized international bibliographic and citation database for the purpose of undertaking bibliometric studies, the quantity and quality of data used for the present study is as good as are the Scopus search tools. In our search strategy, we used Keyword and Article title tags for high recall in search output.